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C₂×#49553 #7705279

• p-group
• nilpotent
• supersolvable
• metabelian
• solvable
• monomial

Aliases

Subgroups

9338 conjugacy classes of subgroups.

Full subgroup data →

Presentation

A minimal faithful permutation representation — 6 generators on 22 points:

(1,2);(4,6)(7,8,11,13)(9,14,10,12);(7,9,11,10)(8,12,13,14)(16,19)(17,21);(3,4)(5,6)(9,10)(12,14)(15,16,18,19)(17,20,21,22);(7,10,11,9)(8,12,13,14)(15,16)(17,20)(18,19)(21,22);(7,8)(9,14)(10,12)(11,13)(15,17)(16,20)(18,21)(19,22)

Conjugacy classes & character table

104 conjugacy classes — view the full character table.

Relationships

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(512, 7612475);